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CONNECTION OF KINETIC MONTE CARLO MODEL FOR SURFACES TO ONE-STEP FLOW THEORY IN 1+1 DIMENSIONS
kinetic Monte Carlo Burton–Cabrera–Frank theory low-density approximation near-equilibrium condition master equation maximum principle
2015/10/16
The Burton–Cabrera–Frank (BCF) theory of step flow has been recognized as a valuable tool for describing nanoscale evolution of crystal surfaces. We formally derive a single-step BCF-type model from a...
A unifying framework for the derivation and analysis of effective classes of one-step methods for ODEs
Ordinary differential equations Runge-Kutta methods one-step methods Hamiltonian problems
2010/12/8
In this paper, we provide a simple framework to derive and analyse several classes of effective one-step methods. The framework consists in the discretization of a local Fourier expansion of the conti...
A Class of Multiderivative Hybrid One-step Methods
hybrid one-step method rational approximation
2007/12/11
This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximation to function exp(q). The algorithms fall into the catalogue of implicit formul...